The present invention relates generally to medical diagnosis, and more particularly relates to magnetic resonance image data acquisition.
Magnetic resonance imaging (MRI) is the method of choice for noninvasive diagnosis of soft tissue disease in humans, and has wide application in cardiovascular diseases. Fast gradient technology has made high-resolution 3D imaging possible, including magnetic resonance angiography (MRA) of coronary and pulmonary arteries. High resolution MRI is primarily impeded by physiologic motion such as respiration and gross patient movement.
Industry responded to the physiologic motion impediment by developing methods to suppress the artifacts caused by physiological motion. Motion correction requires precise motion information. One suppression approach is the navigator method, which detects motion prior to data acquisition and modifies data acquisition accordingly. Navigator techniques use image space navigator echoes for detecting motion during image data acquisition. Physiological motion causes global displacement in the navigator echo and results in a shift of the image space navigator echo compared to an image space reference navigator echo. The accuracy in extracting motion information from navigator echoes is crucial to the effectiveness of the navigator technique. An image space least squares method has been demonstrated to be an accurate method for extracting displacement. The image space least squares algorithm computes the variance for a shifted navigator echo with respect to a reference echo and determines the displacement by locating the shift position that gives the minimum variance. Other methods used include correlation and edge detection methods. However, these methods are time consuming on most host computers of MRI scanners and do not allow flexible real-time control of data acquisition due to the long processing times required.
For effective real-time control of data acquisition, the processing time for processing the navigator echo must be short enough so that there is little motion in the processing duration. When this occurs, the detected motion in the navigator echo is approximately the same as that in the acquired k-space data, thereby allowing effective real-time modification of data acquisition to suppress motion effects.
One approach taken to decrease processing time is to extract linear motion information from raw k-space data. If motion is linear in 3D, only the k-space phase data carries motion information. According to the Fourier shift theorem, a global displacement of d pixels of a reference navigator echo corresponds to a linear phase shift in the k-space data. Equation 1 shows this correspondence.                                           s            dis                    ⁡                      [            x            ]                          =                                                            s                ref                            ⁡                              [                                  x                  +                  d                                ]                                      ⁢                          ⟷              DFT                        ⁢                                          S                dis                            ⁡                              [                k                ]                                              =                                                    S                ref                            ⁡                              [                k                ]                                      ⁢                          exp              ⁡                              (                                  ⅈ                  ⁢                                                            2                      ⁢                                              xe2x80x83                                            ⁢                      π                                        N                                    ⁢                  kd                                )                                                                        [        1        ]            
In equation 1, sref[x] is the reference navigator profile in image space, sdis[x] is the displaced profile in image space, Sref[k] is the reference navigator echo in k-space, Sdis[k] is the displaced echo in k-space, and d is the displacement. Equation 1 illustrates that displacement is proportional to the slope of the phase change in k-space data.
One method to extract displacement information based upon the Fourier shift theorem was proposed by Ahn and Cho. The Ahn and Cho method is fast, requiring only 4N multiplications and 4N additions per displacement estimate. The Ahn and Cho method derives the relation in equation 2 for the displacement d from equation 1:                     d        =                              N                          2              ⁢                              xe2x80x83                            ⁢              π                                ⁢                      (                                          arg                ⁢                                  {                                                                                    S                        dis                        *                                            ⁡                                              [                        k                        ]                                                              ⁢                                                                  S                        dis                                            ⁡                                              [                                                  k                          +                          1                                                ]                                                                              }                                            -                              arg                ⁢                                  {                                                                                    S                        ref                        *                                            ⁡                                              [                        k                        ]                                                              ⁢                                                                  S                        ref                                            ⁡                                              [                                                  k                          +                          1                                                ]                                                                              }                                                      )                                              (        2        )            
In equation 2, arg{xc2x7} is the phase operator, and S*ref[k]Sref[k+1] may be regarded as a kernel of the nearest neighbor correlation.
According to equation 2, only a pair of adjacent points is theoretically sufficient to derive the displacement information. In practice, all data points are contaminated with noise and the displacement derived from two points contains substantial error. To account for noise, all other points in the navigator echo can be averaged to reduce the noise error. Ahn and Cho proposed an average by taking the nearest neighbor correlation prior to the phase operator as shown in equation 3:                                           N                          2              ⁢                              xe2x80x83                            ⁢              π                                ⁢                      arg            ⁢            E                    ⁢                      {                                                            S                  *                                ⁡                                  [                  k                  ]                                            ⁢                              S                ⁡                                  [                                      k                    +                    1                                    ]                                                      }                          =                              N                          2              ⁢                              xe2x80x83                            ⁢              π                                ⁢          arg          ⁢                                    ∑                              k                =                                                      -                    N                                    /                  2                                                                              N                  /                  2                                -                2                                      ⁢                          xe2x80x83                        ⁢                                                            S                  *                                ⁡                                  [                  k                  ]                                            ⁢                              S                ⁡                                  [                                      k                    +                    1                                    ]                                                                                        (        3        )            
E{xc2x7} is the expectation operator and the divider is dropped as it has no effect on the phase. Accordingly, the displacement is:                                           d            ^                    AHN                =                              N                          2              ⁢                              xe2x80x83                            ⁢              π                                ⁢                      (                                          arg                ⁢                                                      ∑                                          k                      =                                                                        -                          N                                                /                        2                                                                                                            N                        /                        2                                            -                      2                                                        ⁢                                      xe2x80x83                                    ⁢                                                                                    S                        dis                        *                                            ⁡                                              [                        k                        ]                                                              ⁢                                                                  S                        dis                                            ⁡                                              [                                                  k                          +                          1                                                ]                                                                                                        -                              arg                ⁢                                                      ∑                                          k                      =                                                                        -                          N                                                /                        2                                                                                                            N                        /                        2                                            -                      2                                                        ⁢                                                                                    S                        ref                        *                                            ⁡                                              [                        k                        ]                                                              ⁢                                                                  S                        ref                                            ⁡                                              [                                                  k                          +                          1                                                ]                                                                                                                  )                                              (        4        )            
It can be seen from equation 4 that points in k-space contribute equally to the final displacement estimate. Consequently, this method is susceptible to noise, particularly contributions from points at the edges of k-space where the noise dominates the signal. Additionally, the Ahn and Cho method is geared towards detecting translation (i.e., displacement). As such, it is suitable for detecting one dimensional motion, but is not effective when detecting general motion.
General motion involves rotation, dilation, and contraction and existing techniques do not work. The rotation, dilation, and contraction effects must be known to correct their motion effects. For example, the widely used pencil beam navigator echo techniques provides a good indication of cardiac motion. However, the pencil beam navigator echo technique cannot detect multiple motion components simultaneously. For example, it cannot effectively monitor the motion of coronary arteries because the motion of chamber blood interferes with the detection of heart motion.
In view of the foregoing, it is a general aim of the present invention to enhance the speed and accuracy of suppressing motion effects in MRI systems.
In that regard, it is also an object of the present invention to minimize noise effects in navigator echoes.
A feature of the present invention is to detect a general motion due to rotation, dilation, and displacement.
A further feature is to detect general motion of coronary arteries due to rotation, dilation, and displacement from data acquired with volume selective excitation.
A further feature is to utilize algorithms which employ weighting factors based on the signal to noise ratio of each point.
In accordance with an embodiment of the instant invention, a method of detecting displacement comprises by fitting a function to the motion-induced phase shift using a k-space weighted least squares minimization to find the displacement where the weighting factor takes into account that the noise in k-space phase data is inversely proportional to the signal to noise ratio.
In accordance with a further embodiment of the instant invention, a method of detecting displacement comprises performing a linear regression on k-space data by fitting a straight line to the motion-induced phase shift using a k-space weighted least squares minimization to find the displacement, and using a weighting factor which takes into account that the noise in k-space phase data is inversely proportional to the signal to noise ratio.
In accordance with a further alternate embodiment of the instant invention, a method of detecting a general motion due to rotation, dilation, and displacement comprises determining a rotation angle and dilation scaling factors from the magnitude k-space data by a least squares minimization. Once the rotation angle and dilation scaling factors are determined, a displacement vector is obtained from the phase data in k-space using a least squares minimization. For example, in one embodiment, general motion of coronary arteries is detected by volume-selective excitation of the arteries. This is accomplished by transmitting a spatial spectral selective pulse to eliminate signals from the chest wall and to excite epicardial fat to produce an excited signal. The coronary motion is detected as described above.
Other objectives and advantages of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawing.